ISI2021-MMA: 19

Question

Suppose $G$ is a cyclic group and $a, b \in G$. There does not exist any $x \in G$ such that $x^{2}=a$. Also, there does not exist an $y \in G$ such that $y^{2}=b$. Then,

• A. there exists an element $g \in G$ such that $g^{2}=a b$.
• B. there exists an element $g \in G$ such that $g^{3}=a b$.
• C. the smallest exponent $k>1$ such that $g^{k}=a b$ for some $g \in G$ is $4 .$
• D. none of the above is true.